Show simple item record

dc.contributor.authorGraves-Morris, Peter R.*
dc.contributor.authorSalam, A.*
dc.date.accessioned2009-05-12T16:17:08Z
dc.date.available2009-05-12T16:17:08Z
dc.date.issued2009-05-12T16:17:08Z
dc.identifier.citationGraves-Morris, P. R., Salam, A.(2002).On the vector epsilon algorithm for solving linear systems of equations. Numerical Algorithms, Vol. 29, no. 1-3, pp. 229-247.en
dc.identifier.urihttp://hdl.handle.net/10454/2637
dc.descriptionNoen
dc.description.abstractThe four vector extrapolation methods, minimal polynomial extrapolation, reduced rank extrapolation, modified minimal polynomial extrapolation and the topological epsilon algorithm, when applied to linearly generated vector sequences are Krylov subspace methods and it is known that they are equivalent to some well-known conjugate gradient type methods. However, the vector -algorithm is an extrapolation method, older than the four extrapolation methods above, and no similar results are known for it. In this paper, a determinantal formula for the vector -algorithm is given. Then it is shown that, when applied to a linearly generated vector sequence, the algorithm is also a Krylov subspace method and for a class of matrices the method is equivalent to a preconditioned Lanczos method. A new determinantal formula for the CGS is given, and an algebraic comparison between the vector -algorithm for linear systems and CGS is also given.en
dc.language.isoenen
dc.subjectExtrapolationen
dc.subjectVector Padé approximationen
dc.subjectProjection methodsen
dc.subjectKrylov subspace methodsen
dc.subjectLanczos methodsen
dc.titleOn the vector epsilon algorithm for solving linear systems of equationsen
dc.status.refereedYesen
dc.typeArticleen
dc.type.versionNo full-text available in the repositoryen
dc.identifier.doihttps://doi.org/10.1023/A:1014832627766


This item appears in the following Collection(s)

Show simple item record